Prepare the pumpkin butter: In a medium saucepan, combine all of the ingredients and mix well. Bring to a low simmer and cook for 20 to 25 minutes, stirring every few minutes, or until the mixture has reduced and thickened. Set aside to cool completely before using.

As the pumpkin butter is cooking, prepare the rolls. In a small saucepan over medium heat, warm the milk until it is body temperature (you can also use the microwave for this). Transfer the warm milk to a large bowl and stir in the yeast. Let the mixture sit until the yeast is dissolved and looks cloudy, about 5 minutes. A few bubbles on the surface is also a good sign that your yeast is ready.

Crack one of the eggs into a small bowl and beat with a fork. Add the beaten egg to the milk-yeast mixture, along with the flour, granulated sugar, salt, and butter. Use a wooden spoon to mix everything together until the dough starts to pull away from the sides of the bowl. If after a minute or two of mixing it doesn’t pull away from the bowl, add a little more flour, 1 Tbsp at a time, until it does. If the dough seems far too dry and impossible to mix, add a little more milk, 1 Tbsp at a time, until it becomes a little more forgiving.

Transfer the dough to a lightly floured work surface. Shape the dough into a large ball and knead it by pressing it with the heel of your hand and pushing it away from you, then immediately pulling it back, folding the top of the dough back on itself. Turn the dough clockwise a little bit each time you push and pull it so that it gets evenly worked, and knead it until its surface is completely smooth and the whole thing feels both solid and soft at the same time. It will take a solid 5 minutes of kneading.

Put the dough back in the large bowl and cover the bowl with plastic wrap. Let the dough sit in the warmest spot in your kitchen until it’s soft and puffy and just about doubled in volume, about 1 hour.

Return the dough to the lightly floured work surface and use a floured rolling pin to roll it into a large oval rectangle measuring roughly 18 in long and 12 in wide. Spread the surface of the dough evenly with 2/3 cup pumpkin butter, leaving a ½-in border. Starting from a long side, roll the dough up tightly so you end up with an 18-in rope. Cut the rope into a dozen even slices.

Line a baking sheet with parchment paper. Arrange the buns, spiraled-butter-side up, on the prepared baking sheet in relatively even rows. The buns should be touching each other but not shoving each other and the seams on the rolls should be facing inward in the “huddle” so that they don’t unravel in the oven. Cover the buns loosely with plastic wrap and let rise at room temperature until they’ve risen a bit and are soft and puffy, about 1 hour. Or, so you can prepare them the night ahead, let them rise at room temperature for just 30 minutes, cover in plastic wrap, and refrigerate overnight. The next morning, pull them out and let return to room temperature, about 1 hour, before proceeding.

Meanwhile, preheat your oven to 350°F. Crack the remaining egg into a small bowl and whisk it with 1 Tbsp water. Uncover the buns and brush them with the egg mixture. Discard whatever egg mixture is left over.

Bake the buns until they’re beautifully browned and the exposed butter is caramelized, 25 to 30 minutes. While the buns are in the oven, in a small bowl, whisk together the powdered sugar, maple syrup, crème fraîche, and vanilla.

Drizzle the hot buns with the crème fraîche mixture. Serve immediately. These buns are best served warm out of the oven.